Characterization of Elastic Waves Induced by Growth of Cracks in the Earth's Crust and its Appliation to Evaluation of Crack Properties

研究了地壳深部裂纹扩展引起的弹性波(声发射)在裂纹(波源)到观测站距离为裂纹大小几十倍的中间区域的特征，并讨论了裂纹大小、位置、取向和变形方式等性质的评价方法。(1)弹性波周向位移谱在w_1/c_2=1.5时出现峰值，其中w为角频率，L为裂纹长度，c_2为剪切波相速度。因此，裂纹尺寸可以估计为L 1.5c_2/(Lw_P)，其中w_p是峰值的角频率。(2)裂纹的方向可以由位移矢量、辐射图样和代表观测点到波源方向的矢量来确定。(3)与剪切型裂纹扩展相比，拉伸型裂纹扩展的弹性波的能量很小。这意味着复合型裂纹的扩展很容易被误解为纯剪切型裂纹扩展，因为拉伸模的贡献很小，并且由于剪切模式的作用很容易被掩埋在弹性波中。(4)纵波到达后的位移矢量指向裂纹扩展发生的部分。在剪切型裂纹扩展中，存在位移量难以分辨的情况。在这种情况下，波源的方向可以由横波到达后的位移矢量来确定。

Characterics of elastic waves (AE:acoustic emission) induced by growth of a crack in the deep earth's crust are studied in the intermediate region where the distance between the crack (the wave source) and an observation station is several ten times the crack size, and, furthermore, methods are discussed for the evaluation of crack properties, such as the size location, orientation and deformation mode. The results obtained in the present work are summarized as follows:(1) Spectrum of the circumferential displacement due to the elastic waves has a peak at wl/c_2=1.5, where w is angular frequency, l a representative length of the crack and c_2 the phase velocity of the shear wave. Therefore, the crack size can be estimated as l 1.5c_2/(lw_p), were w_p is the angular frequency of the peak.(2) The orientation of the crack can be determined by the displacement vector, the radiation pattern and the vector representing the direction from the observation point to the wave source.(3) The energy of the elastic waves due to tensile mode crack growth is very small compared with that due to shear mode crack growth. this means that mixed mode crack growth it apt to be misunderstood as if it is pure shear mode crack growth, since the contribution of tensile mode is very faint and is easily buried in the elastic waves due to shear mode.(4) The displacement vector just after longitudinal wave arrivals points the portion where the crack growth takes place. In shear mode crack growth, there exist the cases that the displacement victor can hardly be distinguished. In such case, the direction of the wave source can be determined by the displacement victor just after shear wave arrivals.